Discrete random variables (Lecture 3)
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expected value of X (mean)
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| Median value |
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| Variance |
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Binomial probability P(X): probability of getting X successes
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Mean, variance and Sd of Binomial
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Poisson distribution probability
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Poisson mean and variance
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Continuous random variables (Lecture 4)
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| f(x) is probability density function (pdf) |
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| Uniform distribution |
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| Normal distribution probability |
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| Exponential distribution |
Introduction to statistics (Lecture 5)
• Nominal – categories only
• Ordinal – categories with some order
• Interval – differences but no natural starting point
• Ratio – differences and a natural starting point
Python code for Binomial and Poisson
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15 | import operator as op
from functools import reduce
import math
def ncr(n, r):
r = min(r, n-r)
numer = reduce(op.mul, range(n, n-r, -1), 1)
denom = reduce(op.mul, range(1, r+1), 1)
return numer // denom
def binomial(n, p, x):
return ncr(n,x)*math.pow(p,x)*math.pow(1-p,n-x)
def poisson(lamda, x):
return math.pow(math.e,-lamda)* (math.pow(lamda,x)/math.factorial(x))
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